Problem: Solve for $x$ and $y$ using substitution. ${5x+3y = 9}$ ${y = -6x-10}$
Explanation: Since $y$ has already been solved for, substitute $-6x-10$ for $y$ in the first equation. ${5x + 3}{(-6x-10)}{= 9}$ Simplify and solve for $x$ $5x-18x - 30 = 9$ $-13x-30 = 9$ $-13x-30{+30} = 9{+30}$ $-13x = 39$ $\dfrac{-13x}{{-13}} = \dfrac{39}{{-13}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = -6x-10}\thinspace$ to find $y$ ${y = -6}{(-3)}{ - 10}$ $y = 18 - 10$ $y = 8$ You can also plug ${x = -3}$ into $\thinspace {5x+3y = 9}\thinspace$ and get the same answer for $y$ : ${5}{(-3)}{ + 3y = 9}$ ${y = 8}$